How can I customize which Tabs show in the Tool shelf/panel?
Afaik the only way is to remove the tab in the python file of the UI toolbar. You can find this file in your blender folder. For me it is:    

C:\Program Files\Blender Foundation\Blender\2.XX\scripts\startup\bl_ui


The name of the file is : space_view3d_toolbar.py

For removing a tab you have to open this file with for example Notepad++.

Then you have to find the tab that you want to remove. If you want to remove the Relations tab for the object mode, you can follow below example. 

First you have to find the section of the code for the object-mode. You can find it with this header in comment:

# ********** default tools for object-mode ****************


Next you have to find the right tab. The name of the tab is in the bl_category, so for our example we have to find this:

bl_category = "Relations"


Now we can get rid of our tab, by either deleting the class of the tab, or by just making it a comment block like this:



You just have to put three quotes like this: """, before and after the class that you want to comment out. I prefer to put the class in comment, so that you can recover it if you do something wrong.

Now you can save your file and restart Blender.